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Annalen der Physik

An exact solution of the dipole photon‐matter interaction

Andreas Osterloh

Published Apr 1, 2013• 0 citations
Publisher

Abstract

Spin-boson interactions are at the heart of modern physics since they bridge the world of photons as described by quantum electrodynamics and that of quantum mechanics of massive objects, like atoms or ions. It is theoretically well understood that for an electric field which is polarized in e.g. x-direction, the electromagnetic dipole interaction produces a term , where is the electric field vector, is the position vector of an electron in the atom, a and are annihilation and creation operators of the electromagnetic field, respectively, and is the Pauli matrix in x-direction, in standard representation . Now, in highly intense light fields far off resonance (), as used in recent experiments, or where the underlying physics itself provides

DOI
10.1002/andp.201300723

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Spin-boson interactions are at the heart of modern physics since they bridge the world of photons as described by quantum electrodynamics and that of quantum mechanics of massive objects, like atoms or ions. It is theoretically well understood that for an electric field which is polarized in e.g. x-direction, the electromagnetic dipole interaction produces a term , where is the electric field vector, is the position vector of an electron in the atom, a and are annihilation and creation operators of the electromagnetic field, respectively, and is the Pauli matrix in x-direction, in standard representation . Now, in highly intense light fields far off resonance (), as used in recent experiments, or where the underlying physics itself provides
E = iJ2 eky/2irnu;k/V (akefi* - a\e'iir) , k where ak, a\ are the annihilation and creation operators of photons with the wave vector k, frequency ujk and polarization ek, satisfying the common boson commutation relations [ak, a}] = 8ki\ V stands for the cavity volume. The free field Hamiltonian has the form k Consider a collection of identical two-level atoms with the upper energy level |1) and the lower energy level |0). The free atomic Hamiltonian reads where sZj — — |0j)(0j| and hcja is the energy separation between two levels. The electric dipole interaction of the cavity field with the atomic system is described by the Hamiltonian where Ej is the electric field at the point fj which corresponds to the position of the j-th atom and dj is the electric dipole operator of this atom given by Here s + i = | l j ) (0j | and s__, = |0 j ) ( l j | are the atomic transition operators and dj = e(lj\f\0j) is the matrix element of the electric dipole momentum (which are assumed to be the same for all the atoms). Note that the operators sZj, s±j obey the algebraic relations for the common Pauli matrices.
The electromagnetic field operators in the Heisenberg picture are found in both the minimal and multipolar forms of nonrelativistic quantum electrodynamics within the electric dipole approximation. These are made up of free- and source-field terms. The free electric- and magnetic-field operators in the two formalisms differ since the creation/annihilation operators are manifestly distinct. Their explicit forms in the Heisenberg picture are given. However, the source fields are formally the same when expressed in terms of dipole moment operators at positive retarded time. The cancellations that lead to this equivalence are presented. In many applications it is necessary to express the operators at retarded time in terms of creation and annihilation operators at the initial time. Explicit expressions for the fields up to second order in terms of the transition dipole moments are given. These enable the formulas for induced dipole moments to be derived within the context of quantum electrodynamics whereas previous derivations have been based on semiclassical electrodynamics.
Matter is coherence held. Photon Light is coherence released. Gravity is coherence constrained. γ = ΔΦ_coh^(U(1), unbound) The photon is not merely a particle of light. It is coherence made light. This disclosure resets an ontological reinterpretation of the photon within the PSOC4(3) framework. It does not reject or replace standard photon physics. The photon remains, operationally, the quantum of the electromagnetic field: a massless boson carrying energy, momentum, polarization, and electromagnetic interaction. The contribution of this paper is interpretive and structural. It proposes that the photon is more deeply understood as the quantum of phase-unbound coherence: the minimal physical event by which coherence becomes light, source structure becomes transmissible, and spatial relation becomes communicable without condensation into mass closure. The paper develops this interpretation through seven figures and a coherent argument linking photon physics, phase, gauge structure, null propagation, information, measurement, visibility, gravity, and quantum-gravitational interpretation. This paper presents the photon as a primary disclosure object within PSOC4(3), the phase-spatial orientation closure framework. Standard physics identifies the photon as the quantum of the electromagnetic field: a massless boson carrying energy, momentum, polarization, and electromagnetic interaction. This paper retains that operational description while proposing a deeper ontological interpretation: the photon is the quantum of phase-unbound coherence. In PSOC4(3), matter is interpreted as coherence held in phase-bound closure, while light is coherence released as propagation. The photon has no rest frame because it is not closure-bound. It is null because its physical disclosure is propagative rather than rest-persistent. It is bosonic because unbound phase coherence is shareable. It carries information because frequency, phase, polarization, timing, direction, and intensity transmit lawful traces of source structure. It is gravitationally affected because gravity constrains coherence disclosure, not merely rest mass. The photon therefore becomes a bridge between quantum theory, relativity, field structure, measurement, visibility, and quantum gravity. It is not merely a particle of light, nor merely a field excitation. It is the minimal visible event by which coherence becomes transmissible appearance without condensation into mass closure. The photon is coherence made light. A photon is usually called a particle of light. More precisely, modern physics describes it as the quantum of the electromagnetic field. This paper accepts that description, but asks a deeper question: What does the photon reveal about reality? The answer proposed here is that the photon is a quantum of coherence. Matter is coherence held. Light is coherence released. Gravity is coherence constrained. A photon is not a tiny solid object flying through space. It has no rest frame. It has no rest mass. It is detected in discrete events, yet propagates as phase and field relation. It carries energy, information, polarization, and source structure across distance. It makes the world visible. In PSOC4(3), the photon is interpreted as phase-unbound coherence: coherence that has not condensed into matter, but remains transmissive as light. In standard relativity, light travels through space. In PSOC4(3), light travels as phase-disclosed space. The photon is therefore not only part of physics. It is part of the ontology of appearance. It is one of the clearest ways reality becomes visible to itself. Keywords Photon, light; coherence, PSOC4(3), phase-spatial closure, U(1), SO(3), electromagnetic field. gauge invariance, null coherence, relativity. quantum theory, measurement, visibility, quantum gravity, phase-unbound coherence